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Touring polygons: An approximation algorithm

Mozafari, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-35926-2_13
  3. Publisher: 2012
  4. Abstract:
  5. In this paper, we introduce a new version of the shortest path problem appeared in many applications. In this problem, there is a start point s, an end point t, an ordered sequence =(S0 = s, S1,...,S k, Sk+1 = t) of sets of polygons, and an ordered sequence =(F0,...,Fk) of simple polygons named fences in such that each fence Fi contains polygons of Si and Si+1. The goal is to find a path of minimum possible length from s to t which orderly touches the sets of polygons of in at least one point supporting the fences constraints. This is the general version of the previously answered Touring Polygons Problem (TPP). We prove that this problem is NP-Hard and propose a precision sensitive FPTAS algorithm of O(k2n2/ ε2) time complexity where n is the total complexity of polygons and fences
  6. Keywords:
  7. Simple polygon ; Approximation algorithm ; Minimum link path ; Touring polygons ; End points ; General version ; NP-hard ; Shortest path problem ; Computational geometry ; Start point ; Time complexity ; Touring polygons ; Computational complexity ; Computational geometry ; Fences ; Graph theory ; Approximation algorithms
  8. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7643 LNCS , 2012 , Pages 110-121 ; 03029743 (ISSN); 9783642359255 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-642-35926-2_13